(* Title: HOL/Nominal/nominal_fresh_fun.ML
Authors: Stefan Berghofer and Julien Narboux, TU Muenchen
Provides a tactic to generate fresh names and
a tactic to analyse instances of the fresh_fun.
*)
(* FIXME proper ML structure! *)
(* FIXME res_inst_tac mostly obsolete, cf. Subgoal.FOCUS *)
(* FIXME proper SUBGOAL/CSUBGOAL instead of cprems_of etc. *)
fun gen_res_inst_tac_term ctxt instf tyinst tinst elim th i st =
let
val thy = Thm.theory_of_thm st;
val cgoal = nth (cprems_of st) (i - 1);
val {maxidx, ...} = Thm.rep_cterm cgoal;
val j = maxidx + 1;
val tyinst' = map (apfst (Logic.incr_tvar j)) tyinst;
val ps = Logic.strip_params (Thm.term_of cgoal);
val Ts = map snd ps;
val tinst' = map (fn (t, u) =>
(head_of (Logic.incr_indexes (Ts, j) t),
fold_rev Term.abs ps u)) tinst;
val th' = instf
(map (apply2 (Thm.ctyp_of thy)) tyinst')
(map (apply2 (Thm.cterm_of thy)) tinst')
(Thm.lift_rule cgoal th)
in
compose_tac ctxt (elim, th', Thm.nprems_of th) i st
end handle General.Subscript => Seq.empty;
(* FIXME proper SUBGOAL/CSUBGOAL instead of cprems_of etc. *)
fun res_inst_tac_term ctxt =
gen_res_inst_tac_term ctxt (curry Thm.instantiate);
fun res_inst_tac_term' ctxt =
gen_res_inst_tac_term ctxt (K Drule.cterm_instantiate) [];
fun cut_inst_tac_term' ctxt tinst th =
res_inst_tac_term' ctxt tinst false (Rule_Insts.make_elim_preserve ctxt th);
fun get_dyn_thm thy name atom_name =
Global_Theory.get_thm thy name handle ERROR _ =>
error ("The atom type "^atom_name^" is not defined.");
(* The theorems needed that are known at compile time. *)
val at_exists_fresh' = @{thm "at_exists_fresh'"};
val fresh_fun_app' = @{thm "fresh_fun_app'"};
val fresh_prod = @{thm "fresh_prod"};
(* A tactic to generate a name fresh for all the free *)
(* variables and parameters of the goal *)
fun generate_fresh_tac ctxt atom_name = SUBGOAL (fn (goal, _) =>
let
val thy = Proof_Context.theory_of ctxt;
(* the parsing function returns a qualified name, we get back the base name *)
val atom_basename = Long_Name.base_name atom_name;
val ps = Logic.strip_params goal;
val Ts = rev (map snd ps);
fun is_of_fs_name T = Sign.of_sort thy (T, [Sign.intern_class thy ("fs_"^atom_basename)]);
(* rebuild de bruijn indices *)
val bvs = map_index (Bound o fst) ps;
(* select variables of the right class *)
val vs = filter (fn t => is_of_fs_name (fastype_of1 (Ts, t)))
(Misc_Legacy.term_frees goal @ bvs);
(* build the tuple *)
val s = (Library.foldr1 (fn (v, s) =>
HOLogic.pair_const (fastype_of1 (Ts, v)) (fastype_of1 (Ts, s)) $ v $ s) vs)
handle TERM _ => HOLogic.unit;
val fs_name_thm = get_dyn_thm thy ("fs_"^atom_basename^"1") atom_basename;
val at_name_inst_thm = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
val exists_fresh' = at_name_inst_thm RS at_exists_fresh';
(* find the variable we want to instantiate *)
val x = hd (Misc_Legacy.term_vars (Thm.prop_of exists_fresh'));
in
fn st =>
(cut_inst_tac_term' ctxt [(x,s)] exists_fresh' 1 THEN
rtac fs_name_thm 1 THEN
etac exE 1) st
handle List.Empty => all_tac st (* if we collected no variables then we do nothing *)
end) 1;
fun get_inner_fresh_fun (Bound j) = NONE
| get_inner_fresh_fun (v as Free _) = NONE
| get_inner_fresh_fun (v as Var _) = NONE
| get_inner_fresh_fun (Const _) = NONE
| get_inner_fresh_fun (Abs (_, _, t)) = get_inner_fresh_fun t
| get_inner_fresh_fun (Const (@{const_name Nominal.fresh_fun},
Type(@{type_name fun},[Type (@{type_name fun},[Type (T,_),_]),_])) $ u) = SOME T
| get_inner_fresh_fun (t $ u) =
let val a = get_inner_fresh_fun u in
if a = NONE then get_inner_fresh_fun t else a
end;
(* This tactic generates a fresh name of the atom type *)
(* given by the innermost fresh_fun *)
fun generate_fresh_fun_tac ctxt = SUBGOAL (fn (goal, _) =>
let
val atom_name_opt = get_inner_fresh_fun goal;
in
case atom_name_opt of
NONE => all_tac
| SOME atom_name => generate_fresh_tac ctxt atom_name
end) 1;
(* Two substitution tactics which looks for the innermost occurrence in
one assumption or in the conclusion *)
val search_fun = curry (Seq.flat o uncurry EqSubst.searchf_bt_unify_valid);
val search_fun_asm = EqSubst.skip_first_asm_occs_search EqSubst.searchf_bt_unify_valid;
fun subst_inner_tac ctxt = EqSubst.eqsubst_tac' ctxt search_fun;
fun subst_inner_asm_tac_aux i ctxt = EqSubst.eqsubst_asm_tac' ctxt search_fun_asm i;
(* A tactic to substitute in the first assumption
which contains an occurrence. *)
fun subst_inner_asm_tac ctxt th =
curry (curry (FIRST' (map uncurry (map uncurry (map subst_inner_asm_tac_aux
(1 upto Thm.nprems_of th)))))) ctxt th;
fun fresh_fun_tac ctxt no_asm = SUBGOAL (fn (goal, i) =>
(* Find the variable we instantiate *)
let
val thy = Proof_Context.theory_of ctxt;
val abs_fresh = Global_Theory.get_thms thy "abs_fresh";
val fresh_perm_app = Global_Theory.get_thms thy "fresh_perm_app";
val simp_ctxt =
ctxt addsimps (fresh_prod :: abs_fresh)
addsimps fresh_perm_app;
val x = hd (tl (Misc_Legacy.term_vars (Thm.prop_of exI)));
val atom_name_opt = get_inner_fresh_fun goal;
val n = length (Logic.strip_params goal);
(* Here we rely on the fact that the variable introduced by generate_fresh_tac *)
(* is the last one in the list, the inner one *)
in
case atom_name_opt of
NONE => all_tac
| SOME atom_name =>
let
val atom_basename = Long_Name.base_name atom_name;
val pt_name_inst = get_dyn_thm thy ("pt_"^atom_basename^"_inst") atom_basename;
val at_name_inst = get_dyn_thm thy ("at_"^atom_basename^"_inst") atom_basename;
fun inst_fresh vars params i st =
let val vars' = Misc_Legacy.term_vars (Thm.prop_of st);
val thy = Thm.theory_of_thm st;
in case subtract (op =) vars vars' of
[x] =>
Seq.single (Thm.instantiate ([], [(Thm.cterm_of thy x, Thm.cterm_of thy (fold_rev Term.abs params (Bound 0)))]) st)
| _ => error "fresh_fun_simp: Too many variables, please report."
end
in
((fn st =>
let
val vars = Misc_Legacy.term_vars (Thm.prop_of st);
val params = Logic.strip_params (nth (Thm.prems_of st) (i-1))
(* The tactics which solve the subgoals generated
by the conditionnal rewrite rule. *)
val post_rewrite_tacs =
[rtac pt_name_inst,
rtac at_name_inst,
TRY o SOLVED' (NominalPermeq.finite_guess_tac simp_ctxt),
inst_fresh vars params THEN'
(TRY o SOLVED' (NominalPermeq.fresh_guess_tac simp_ctxt)) THEN'
(TRY o SOLVED' (asm_full_simp_tac simp_ctxt))]
in
((if no_asm then no_tac else
(subst_inner_asm_tac ctxt fresh_fun_app' i THEN (RANGE post_rewrite_tacs i)))
ORELSE
(subst_inner_tac ctxt fresh_fun_app' i THEN (RANGE post_rewrite_tacs i))) st
end))
end
end)